# Phase 8 Part E: Safe Rate Mechanism Robustness

Testing whether demographics survive additional controls for GDP growth and investment/GDP jointly.

| Model | Dep Var | Z₁ | p(Z₁) | rgdp_growth | inv/GDP | R² | N |
|---|---|---|---|---|---|---|---|
| E1: Baseline Z → 10y | real_bond_10y | 43.72** | 0.0154 | -0.033 | — | 0.108 | 803 |
| E2: Z + growth only → 10y | real_bond_10y | 44.45** | 0.0119 | -0.051 | — | 0.129 | 907 |
| E3: Z + growth + inv → 10y | real_bond_10y | 51.91*** | 0.0014 | -0.035 | -0.180 | 0.235 | 907 |
| E4: Z + full + inv → 10y | real_bond_10y | 47.98*** | 0.0072 | -0.032 | -0.044 | 0.154 | 803 |
| E1: Baseline Z → 3m | real_short_3m | 60.07*** | 0.0043 | -0.060 | — | 0.005 | 813 |
| E2: Z + growth only → 3m | real_short_3m | 62.22*** | 0.0006 | -0.049 | — | 0.177 | 910 |
| E3: Z + growth + inv → 3m | real_short_3m | 64.27*** | 0.0004 | -0.045 | -0.030 | 0.182 | 910 |
| E4: Z + full + inv → 3m | real_short_3m | 55.41*** | 0.0095 | -0.063 | 0.061 | -0.027 | 813 |

*Demographics survive controlling for GDP growth and investment/GDP, both individually and jointly. The demographic effect on safe rates is not obviously mediated by contemporaneous investment — though investment/GDP is an equilibrium object, so this test is suggestive rather than definitive.*
